Non-Local Boundary Conditions for Massless Spin-1/2 Fields

TL;DR

This paper investigates the effects of non-local spectral boundary conditions on massless spin-1/2 fields in a bounded Euclidean space, revealing the vanishing of the conformal anomaly and implications for supergravity models.

Contribution

It introduces a spectral-type non-local boundary condition analysis for massless spin-1/2 fields and demonstrates the conformal anomaly vanishes under these conditions, extending to supergravity models.

Findings

Conformal anomaly vanishes with spectral boundary conditions.

Non-local boundary conditions can be analyzed using ζ-function regularization.

Results suggest potential applications in supergravity models.

Abstract

This paper studies the 1-loop approximation for a massless spin-1/2 field on a flat four-dimensional Euclidean background bounded by two concentric 3-spheres, when non-local boundary conditions of the spectral type are imposed. The use of $\zeta$-function regularization shows that the conformal anomaly vanishes, as in the case when the same field is subject to local boundary conditions involving projectors. A similar analysis of non-local boundary conditions can be performed for massless supergravity models on manifolds with boundary, to study their 1-loop properties.